Finite Markov chains with absorbing states and mis-specified random effects: application to cognitive data
Bibliographic record
Abstract
Finite Markov chains with absorbing states are valuable tools for analyzing longitudinal data with categorical responses. However, defining the one-step transition probabilities in terms of fixed and random effects presents challenges due to the large number of unknown parameters involved. To address this, we employ a marginal model to estimate the fixed effects across various choices of the distribution governing the random effects. Subsequently, we utilize an h-likelihood method to estimate the random effects based on these fixed effect estimates. The estimation approach is applied to analyze longitudinal cognitive data from the Nun Study. Our findings highlight that the fixed effects remain relatively robust across a wide range of assumptions. However, the analysis of random effects utilizing tools such as AIC, Q-Q plots, and gradient plots appears to be sensitive to mis-specifications in the distribution of the random effects. Our proposed approach allows researchers to verify the assumptions of random effects and provides more accurate estimation of these effects. Additionally, the precisely estimated random effects enable researchers to identify individuals at high risk for absorbing states (e.g. incurable diseases) and to determine the progression rates for certain diseases.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".